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River 9♥: Hero checks, BTN bets 32bb into 48bb

Multi-way River | 3-way: CO | 100bb effective | Difficulty: Expert

Players in hand: Hero (CO), BTN, BB

Hero hand

K♠K♣

Board

Q♥J♠T♦5♣9♥

Action so far:
PF: 3-way, Hero opened KK from CO
Flop Q♥J♠T♦: Hero c-bets, BTN calls
Turn 5♣: Hero barrels, BTN calls
River 9♥: Hero checks, BTN bets 32bb into 48bb

Pot: 48bb   To call: 32bb

Villain range: BTN flat range that calls flop and turn: AK (now nut straight), KQ, KJ, KT, QJ, QT, JT, sets 99/55/TT slowplayed. Bluffs: busted Th8h, 8h7h, A-high spades

Your move: